On multipoint constraints in FETI methods

Abstract

FETI (finite element tearing and interconnecting) based domain decomposition methods are well-established massively parallel methods for solving huge linear systems arising from discretizing partial differential equations. The first steps of FETI decompose the domain into nonoverlapping subdomains, discretize the subdomains using matching grids, and interconnect the adjacent variables by multipoint constraints. However, the multipoint constraints enforcing identification of the corners’ variables do not have a unique representation and their proper choice and modification can improve the performance of FETI. Here, we briefly review the main options, including orthogonal, fully redundant, or localized constraints, and use the basic linear algebra and spectral graph theory to examine the quantitative effect of their choice on the effective control of the feasibility error and rate of convergence of FETI.